In this Markdown presentation, I will present some results of the pilot simulation study that I did for my thesis. My thesis is about efficient audit sample selection. In the pilot simulation study, I compare two methods for efficient sample selection against each other: the sample size approach and the deviance approach. Here follows an overview of some preliminary results.
2023-01-21
Thesis Presentation
Results in a table
This table shows the number of iterations and the deviance before and after in the first 100 datasets.
Results in a Figure
Results in an Interactive Figure
The Code to Create the Interactive Figure
library(plotly)
p <- ggplot(aes(x = condition, y = added_units, fill = study), data = total_results) +
geom_boxplot() +
theme_classic() +
scale_fill_grey() +
xlab("Condition") +
ylab("Added Units") +
theme(legend.title = element_blank(), text = element_text(size = 18),
axis.text.x = element_text(angle = -30, hjust = 0))
ggplotly(p)
The Problem in an Equation
The minimization procedure can be written as follows: \[min\{\sum_{i,j} \delta_{ij}^+ + \sum_{i,j} \delta_{ij}^-\}\] under constraints \[m_{ij1} = n_{ij1} + \delta_{ij}^+ - \delta_{ij}^-;\] \[m_{ij0} = n_{ij0} - \delta_{ij}^+ + \delta_{ij}^-;\] \[D \leq \chi_{I(J-1)}^2 (1-\alpha);\] \[0 \leq \delta_{ij}^+ \leq n_{ij0};\] \[0 \leq \delta_{ij}^- \leq n_{ij1}.\]